Periodic moving coherent structures (particles) are well known in parallel string processing (SP) performed by cellular automata (CAs). In 1986 the discrete soliton-like objects were shown in a filter CA model that performs serial SP. Then, some other systems that support discrete solitons were proposed in nonlinear physics. Now there are iterated arrays, filter CAs, soliton CAs, higher order CAs, sequentially updated CAs, integrable CAs, IIR digital filters, filter transducers, ultradiscrete soliton equations (KdV, KP, L-V), and fast rules. Also, box-ball systems, crystal systems and affine Lie algebras were introduced recently. We show a unified approach to all these processing mechanisms. They are based on iterated automata maps (IAMs). Automaton equivalents to various systems differ on their organization of memory. We show the automata that use various finite and/or infinite memories: shift registers, counters, stacks, FIFO, lists, and pipelines of counters. In our approach the IAMs mimic transmitting media, while filtrons describe propagating coherent disturbances. We mention also various phenomena of interacting filtrons.